8 papers
Relative stability, relative categoricity and internal covers
Mostafa Mirabi, Anand Pillay
Let be a countable complete theory with a distinguished unary predicate , and let be the theory of the -parts of models of with the induced structure. is…
Remarks on relative categoricity
Anand Pillay
The paper is partly a survey with historical background and references, partly provides the opportunity to put in print some unpublished early work, and partly has new results. A s…
On groups definable in -adically closed fields
Anand Pillay, Ningyuan Yao, Zhentao Zhang
This paper is about the / decomposition for groups definable in -adically closed fields. It is proved that for definably amenable, has a definable normal $…
Definable Galois theory for bimeromorphic geometry
Rahim Moosa, Anand Pillay
The outlines of a "Galois theory" for bimeromorphic geometry is here developed, via the study of model-theoretic definable binding groups in the theory CCM of compact complex space…
The number of countable models of first-order theories
Anand Pillay, Predrag Tanović
Throughout, denotes a complete first-order theory in a countable language that has infinite models and denotes the number of countable models of , up to…
On groups definable in geometric fields with generic derivations
Anand Pillay, Françoise Point, Silvain Rideau-Kikuchi
We study groups definable in existentially closed geometric fields with commuting derivations. Our main result is that such a group can be definably embedded in a group interpretab…
An arithmetic algebraic regularity lemma
Anand Pillay, Atticus Stonestrom
We give an 'arithmetic regularity lemma' for groups definable in finite fields, analogous to Tao's 'algebraic regularity lemma' for graphs definable in finite fields. More specific…
Automorphism groups of prime models, and invariant measures
Anand Pillay
We adapt the notion of a (relatively) definable subset of Aut(M) when M is a saturated model to the case Aut(M/A) when M is atomic and strongly omega-homogeneous over A. We discuss…